= Angle between vectors
{title2=$\cos\theta=\boldsymbol a\cdot\boldsymbol b/(\|\boldsymbol a\|\|\boldsymbol b\|)$}
For nonzero real <vectors> in a <Euclidean space>, their <angle> $\theta\in[0,\pi]$ is determined by the displayed <dot product> formula. The <Cauchy-Schwarz inequality> puts the quotient in $[-1,1]$, so the inverse cosine is defined. Perpendicular <vectors> have angle $\pi/2$, parallel vectors pointing the same way have angle zero, and those pointing in opposite directions have angle $\pi$. A zero vector has no uniquely defined direction and hence no angle by this definition.
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